The mean sea level (MSL) trend at Hornbaek, Denmark is
0.37 mm/year
with a 95% confidence interval of ± 0.22 mm/year,
based on monthly mean sea level data from 1898
to 2011.&ddagger;
That is equivalent to a change of 0.12 feet in 100 years.
(R‑squared =
(?))

The plot shows the monthly mean sea level without
the regular seasonal fluctuations due
to coastal ocean temperatures, salinities, winds, atmospheric pressures, and ocean currents. By default, the long-term linear
trend is also shown, in red, along with its 95% confidence interval. The plotted values are relative
to the most recent Mean Sea Level datum
established by NOAA CO-OPS.

†Calculation of Confidence Intervals and Prediction Intervals
for monthly Mean Sea-Level (MSL) is complicated by the fact that MSL measurement data is serially autocorrelated. That means
each month's MSL measurement is correlated, to an extent which varies by location, with the MSL measurements of the previous
and next months. That means there are effectively fewer independent measurements, which would cause a naive confidence interval
calculation to underestimate the breadth of the intervals. The code here follows the method of Zervas 2009, “Sea Level
Variations of the United States 1854-2006,”NOAA Technical Report NOS CO-OPS 053, p. 15-24, to
account for autocorrelation, when calculating confidence intervals and prediction intervals. That isn't the only way to do it,
though, and one of the items on my to-do list is to examine an alternative approach suggested by Willis Eschenbach.